№3. Решите уравнение: 1) 4x + 8 = 2x - 6; 2) 5(x + 12) = -3(x - 2); 3) \(\frac{5}{6}\)(12x - 6) - \(\frac{4}{9}\)(9x + 27) = 3,5(x + 10); 4) \(\frac{x+5}{8} = \frac{2x-7}{18}\)

Решение:

• 1) \( 4x + 8 = 2x - 6 \)
• \( 4x - 2x = -6 - 8 \)
• \( 2x = -14 \)
• \( x = \frac{-14}{2} \)
• \( x = -7 \)
• 2) \( 5(x + 12) = -3(x - 2) \)
• \( 5x + 60 = -3x + 6 \)
• \( 5x + 3x = 6 - 60 \)
• \( 8x = -54 \)
• \( x = \frac{-54}{8} \)
• \( x = -6,75 \)
• 3) \( \frac{5}{6}(12x - 6) - \frac{4}{9}(9x + 27) = 3,5(x + 10) \)
• \( 10x - 5 - 4x - 12 = 3,5x + 35 \)
• \( 6x - 17 = 3,5x + 35 \)
• \( 6x - 3,5x = 35 + 17 \)
• \( 2,5x = 52 \)
• \( x = \frac{52}{2,5} \)
• \( x = 20,8 \)
• 4) \( \frac{x+5}{8} = \frac{2x-7}{18} \)
• \( 18(x + 5) = 8(2x - 7) \)
• \( 18x + 90 = 16x - 56 \)
• \( 18x - 16x = -56 - 90 \)
• \( 2x = -146 \)
• \( x = \frac{-146}{2} \)
• \( x = -73 \)

Ответ: 1) -7; 2) -6,75; 3) 20,8; 4) -73.